The Nerazzurri failed to qualify for any European competition last season having finished ninth in Serie A, while they currently occupy the final Europa League spot this year.
Just two points separate them from sixth-placed Parma and another season without continental football, and Fassone admitted that missing out again would be a blow to both their ambitions as a club and their financial position.
"It's obvious that in the last few months, our club president has requested as an aim to return to Europe," Fassone told the club's official website.
"It would be problematic not to qualify for continental competition for a second straight year, not just for the work we are doing but also from a financial standpoint."
Inter's next match comes against Parma on Saturday as the San Siro plays host to a crucial encounter in the race for fifth.